It is possible to construct designs which do not have these properties.
This will happen, for example, if reference standards are only compared
among themselves and test items are only compared among themselves
without any intercomparisons.

Practical considerations determine a 'good' design

We do not apply 'optimality' criteria in constructing calibration
designs because the construction of a 'good' design depends on many
factors, such as convenience in manipulating the test items, time,
expense, and the maximum load of the instrument.

The number of measurements should be small.

The degrees of freedom should be greater than three.

The standard deviations of the estimates for the test items
should be small enough for their intended purpose.